# Robust Kalman Filtering under Model Perturbations

arXiv: https://arxiv.org/abs/1508.01906 · HTML: https://mlsanity.com/paper/1508.01906/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Aug 2015.

## Built on by (most cited first, 4 of 4)

- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [Nash Equilibria, Regularization and Computation in Optimal Transport-Based Distributionally Robust Optimization](https://mlsanity.com/paper/2303.03900/) (2023)
- [A Geometric Unification of Distributionally Robust Covariance Estimators: Shrinking the Spectrum by Inflating the Ambiguity Set](https://mlsanity.com/paper/2405.20124/) (2024)
- [Dynamic Perturbation-Adaptive Adversarial Training on Medical Image Classification](https://mlsanity.com/paper/2403.06798/) (2024)

## Abstract (arXiv)

We consider a family of divergence-based minimax approaches to perform robust filtering. The mismodeling budget, or tolerance, is specified at each time increment of the model. More precisely, all possible model increments belong to a ball which is formed by placing a bound on the Tau-divergence family between the actual and the nominal model increment. Then, the robust filter is obtained by minimizing the mean square error according to the least favorable model in that ball. It turns out that the solution is a family of Kalman like filters. Their gain matrix is updated according to a risk sensitive like iteration where the risk sensitivity parameter is now time varying. As a consequence, we also extend the risk sensitive filter to a family of risk sensitive like filters according to the Tau-divergence family.